A certain number of artisans can complete a shoe fabrication consignment in 16 days. 8 additional artisans had to be deployed for the same consignment and together they completed it in 4 days less than the earlier estimate. The number of artisans initially employed was

### Concept & Work Equivalence Principle When the total amount of work remains constant, the number of workers is inversely proportional to the number of days taken. $$ M_1 \times D_1 = M_2 \times D_2 $$ ### Step-by-Step Solution 1. **Define the initial state:** Let the initial number of artisans be $x$. They take 16 days. - Total Work = $x \times 16$ 2. **Define the new state:** 8 additional artisans are deployed, making the total number $(x + 8)$. They complete the work in 4 days less, meaning it takes $16 - 4 = 12$ days. - Total Work = $(x + 8) \times 12$ 3. **Equate the work:** - $16x = 12(x + 8)$ 4. **Solve for $x$:** - $16x = 12x + 96$ - $4x = 96$ - $x = 24$ ### Exam Strategy & Shortcut Use the ratio method. The ratio of days taken is $16 : 12$, which simplifies to $4 : 3$. Since days and workers are inversely proportional, the ratio of workers must be $3 : 4$. The difference in the ratio is 1 unit, which corresponds to the 8 additional artisans. Initial workers = 3 units = $3 \times 8 = 24$. ### Common Pitfall Misinterpreting "4 days less" as completing the work in exactly 4 days. Always subtract the saved days from the original estimate ($16 - 4 = 12$). ### Final Answer Therefore, the correct answer is **24**.